We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the Hamiltonian and bound state properties of the two-body inter-layer dipolar potential are used to adjust this effective interaction. To model the intra-layer repulsion of the polar molecules, we introduce a repulsive inter-molecule harmonic potential and discuss how its strength can be related to the real dipolar potential. However, to explore different structures with more than one molecule in each layer, we treat the repulsive harmonic strength as an independent variable in the problem. Single chains containing one molecule in each layer, as well as multi-chain structures in many layers are discussed and their energies and radii determined. We extract the normal modes of the various systems as measures of their volatility and eventually of instability, and compare our findings to the excitations in crystals. We find modes that can be classified as either chains vibrating in phase or as layers vibrating against each other. The former correspond to acoustic and the latter to optical phonons. For the acoustic modes, our model predicts a smaller sound speed than one would naively get from expansion of the dipolar potential to second order around the origin. Instabilities can occur for large intra-layer repulsion and produce diverging amplitudes of molecules in the outer layers, and our model predicts how the breakup takes places. Lastly, we consider experimentally relevant regimes to observe the structures. The harmonic model considered here predicts that for the multi-layer systems under current study chains with one molecule in each layer are always bound whereas two chains comprised of two molecules in each layer will not be bound. However, since realistic systems have external confinement prevention the molecules from escaping to infinity, we still expect the unstable modes to show up as resonances in the dynamics.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics